Answer:
The equation of parabola is [tex]y^2=-32x[/tex].
Step-by-step explanation:
It is given that the directrix of the parabola is x = 8 and focus is (-8, 0).
Since directrix is x=8, which a vertical line therefore the parabola is algo the x-axis.
The standard for of the parabola is
[tex](y-k)^2=4p(x-h)[/tex]
Where (h+p,k) is focus and [tex]x=h-p[/tex] is the directrix.
Since focus of the parabola is (-8,0)
[tex](h+p,k)=(-8,0)[/tex]
[tex]k=0[/tex]
[tex]h+p=-8[/tex] .... (1)
The directrix of the parabola is x= 8
[tex]h-p=8[/tex] .... (2)
Add equation (1) and (2).
[tex]2h=0[/tex]
[tex]h=0[/tex]
Put this value in equation 1.
[tex]p=-8[/tex]
Therefore h=0, k=0 and p=-8.
[tex](y-0)^2=4(-8)(x-0)[/tex]
[tex]y^2=-32x[/tex]
Therefore equation of parabola is [tex]y^2=-32x[/tex].
